Suppose a Monopsony facing the following labor supply given by curve L = 10W, where L is the number of workers and W = hourly wage. a) Express the hourly wage in terms of the number of workers (L). b) Provide an expression of total labor cost in terms of the number of workers (L) c) Express the marginal expense of labor (MEL) in terms of the number of workers. d) Suppose the marginal revenue product of labor ((MRPL) = 7 – L. What is the level of workers that maximizes the monophony’s profit? What is the wage paid by the monopsony at the profit maximizing level of labor?

The answer is given below

Explanation:

a. Express the hourly wage in terms of the number of workers (L).

From the question, the labor supply given by L = 10W, where,

L = number of workers

W = hourly wage

Since L = 10W

Divide both side by 10

L/10 = 10W/10

W = L/10

The hourly wage(W) expressed in terms of the number of workers(L) is L/10.

b. Provide an expression of total labor cost in terms of the number of workers (L).

Total labor cost = L × W

Since W = L/10,

Total labor cost = L × L/10

= L²/10

c. Express the marginal expense of labor (MEL) in terms of the number of workers.

Marginal expense of labor will be gotten when we find the derivative of the total labor cost.

Total labor cost = L²/10

MEL = 2L/10

We can reduce to lowest term

MEL = L/5

d. Suppose the marginal revenue product of labor ((MRPL) = 7 – L. What is the level of workers that maximizes the monophony’s profit? What is the wage paid by the monopsony at the profit maximizing level of labor?

Marginal revenue product of labor (MRPL) = 7 – L

At equilibrium, the marginal revenue product of labor (MRPL) will be equal to the marginal expense of labor(MEL)

MRPL = MEL

7 - L = L/5

Cross multiply

5(7 - L) = L

35 - 5L = L

35 = L + 5L

35 = 6L

L = 35/6

L = 5.83 = 6 Approximately

The level of workers that maximizes the monophony’s profit will be approximately 6.

Wages paid = L/10

= 6/10

= 0.6

The wage paid by the monopsony at the profit maximizing level of labor will be 0.6.

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